What is the optimal time complexity of solving Greatest Common Divisor?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Greatest Common Divisor?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Greatest Common Divisor?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Greatest Common Divisor?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Python BasicsEasy

Greatest Common Divisor

Learn how to solve the 'Greatest Common Divisor' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function gcd(a, b) that takes two non-negative integers a and b (not both zero) and returns their Greatest Common Divisor (GCD) using the Euclidean algorithm. The GCD is the largest number that divides both a and b.

The Euclidean algorithm works by repeatedly replacing the larger number with the remainder of dividing the larger by the smaller, until the remainder is 0. The last non-zero remainder is the GCD.

Constraints

•0 <= a, b <= 10^6
•a and b are not both zero

Examples

Example 1

Input

gcd(48, 18)

Output

Explanation

48 % 18 = 12, then 18 % 12 = 6, then 12 % 6 = 0. So GCD is 6.

Example 2

Input

gcd(56, 98)

Output

Explanation

98 % 56 = 42, 56 % 42 = 14, 42 % 14 = 0. So GCD is 14.

Example 3

Input

gcd(0, 5)

Output

Explanation

GCD(0, n) = n for any positive n.

Need a Hint?

Use simple arithmetic operators (like modulo `%`, division `//`), conditional checks, or loops to inspect number properties.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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